Finite Group Databasebeta

← #25066733

Subgroups — #25066733

Order 11008.

638 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144603C211yesmaximal, characteristic
2#19143692C211yesmaximal, characteristic, complemented
3#19143619C211yesmaximal, characteristic
4#19133449C212yesmaximal, complemented
5#19133428C212yesmaximal, complemented
6#19133404C212yesmaximal, complemented
7#19133398C212yesmaximal, complemented
8#19133376C211yesmaximal, characteristic, complemented
9#19133017C211yesmaximal, characteristic, complemented
10#19132892C211yesmaximal, characteristic, complemented
11C43×#1490C211yesmaximal, characteristic
12#14583456C2211yescharacteristic
13#14583229C412yes—
14#14583189C412yes—
15#14583104C412yes—
16#14583050C412yes—
17#14583027—22no—
18#14583026C2212yescomplemented
19#14583023C2212yescomplemented
20C4×#10621883C2212yes—
21C4×#10621883C2212yes—
22D4×C43⋊C8—22no—
23D4×C43⋊C8C2212yes—
24D4×C43⋊C8C2212yes—
25#14582957—22no—
26#14582952C2211yescharacteristic
27#14582952C2211yescharacteristic
28#14582952C2211yescharacteristic
29C2×C22⋊(C43⋊C8)—22no—
30#14582651C2212yescomplemented
31#14582649C2212yescomplemented
32#14582631C2212yescomplemented
33#14582631C2212yescomplemented
34#14582621C2211yescharacteristic, complemented
35#14582621C2211yescharacteristic, complemented
36#14582620C2211yescharacteristic, complemented
37C8×C43⋊C8C2211yescharacteristic, complemented
38C2×C4×D4×C43C2211yescharacteristic
39C43×#432C2211yescharacteristic
40C4×M16×C43C2211yescharacteristic
41C43×D4⋊C8C2212yes—
42C43×D4⋊C8C2212yes—
43C2×#10621883C2×C412yes—
44C2×#10621883C2×C412yes—
45C22×C43⋊C8—22no—
46C22×C43⋊C8—22no—
47#13063325C2×C411yescharacteristic
48#13063325C2×C411yescharacteristic
49#13063317—21no—
50#13063304—21no—
51#13063304C2×C412yes—
52C4×Dic86—21no—
53C4×Dic86C2312yes—
54#13063284—21no—
55#13063256C2×C412yes—
56#13063256C2×C412yes—
57C4⋊(C43⋊C8)C2×C412yes—
58C4⋊(C43⋊C8)D412yes—
59C4⋊(C43⋊C8)C2312yes—
60Dic43⋊C8—22no—
61Dic43⋊C8—22no—
62#13063248C2×C412yes—
63#13063248C2×C412yes—
64#13063246C2×C412yes—
65#13063246C2×C412yes—
66C22⋊(C43⋊C8)—21no—
67C22⋊(C43⋊C8)—22no—
68C22⋊(C43⋊C8)—22no—
69C22⋊(C43⋊C8)C2×C412yes—
70C22⋊(C43⋊C8)D412yes—
71#13063235—22no—
72C4×C43⋊C8—21no—
73C4×C43⋊C8C2311yescharacteristic
74C4×C43⋊C8C2311yescharacteristic
75C4×C43⋊C8C2311yescharacteristic
76C4×C43⋊C8C2311yescharacteristic
77C8×Dic43—22no—
78C22×D4×C43C2×C411yescharacteristic
79C23×C4×C43—21no—
80C2×M16×C43—21no—
81C4×D4×C43—21no—
82C4×D4×C43—21no—
83C4×D4×C43C2×C412yes—
84C4×D4×C43C2312yes—
85C2×C4⋊C4×C43C2×C411yescharacteristic
86C2×C22⋊C4×C43—21no—
87C2×C42×C43C2311yescharacteristic
88C4⋊C8×C43C2312yes—
89C22⋊C8×C43—21no—
90#97×C43—21no—
91#97×C43—21no—
92C4×C8×C43C2311yescharacteristic
93C4×C8×C43C2311yescharacteristic
94C24×C43—21no—
95C2×D4×C43—24no—
96C2×D4×C43—21no—
97C2×D4×C43C22×C412yes—
98C22×C4×C43—22no—
99C22×C4×C43—22no—
100C22×C4×C43—21no—
101C22×C4×C43—82no—
102C22×C4×C43C22×C411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43#4111yescharacteristic
105C2×Dic86—21no—
106C2×Dic86C22×C412yes—
107M16×C43—42no—
108C2×C8×C43—21no—
109C2×C8×C43—22no—
110C2×C8×C43—21no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43C22×C412yes—
113C22⋊C4×C43—22no—
114C22⋊C4×C43—22no—
115C42×C43C22×C411yescharacteristic
116C42×C43C2×D411yescharacteristic
117C42×C43#4111yescharacteristic
118C42×C43C2411yescharacteristic
119C22⋊Dic43—22no—
120#10621883—24no—
121#10621883—24no—
122C4⋊Dic43—21no—
123C4⋊Dic43—21no—
124C4⋊Dic43—21no—
125C4⋊Dic43C22×C412yes—
126Dic43⋊C4—22no—
127Dic43⋊C4—22no—
128C4×Dic43—22no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—82no—
131C2×C43⋊C8—82no—
132C2×C43⋊C8C22×C412yes—
133C2×C43⋊C8C22×C412yes—
134C2×C43⋊C8C2×D412yes—
135C2×C43⋊C8C2×D412yes—
136C23×C43—24no—
137C23×C43—22no—
138C23×C43—81no—
139C23×C43—81no—
140C23×C43C4×D411yescharacteristic
141D4×C43—24no—
142D4×C43—22no—
143D4×C43#13114yes—
144C2×C4×C43—22no—
145C2×C4×C43—22no—
146C2×C4×C43—22no—
147C2×C4×C43—41no—
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43—82no—
151C2×C4×C43—81no—
152C2×C4×C43C4×D411yescharacteristic
153C2×C4×C43C4×D411yescharacteristic
154C2×C4×C43C4×D411yescharacteristic
155C2×C4×C43C23×C411yescharacteristic
156C2×C4×C43C22×D411yescharacteristic
157C2×C4×C43C2×#4111yescharacteristic
158C2×Dic43—22no—
159C2×Dic43—22no—
160Dic86—22no—
161Dic86—22no—
162Dic86—81no—
163C8×C43—22no—
164C8×C43—41no—
165C8×C43—42no—
166C43⋊C8—22no—
167C43⋊C8—22no—
168C43⋊C8—22no—
169C43⋊C8—22no—
170C43⋊C8—42no—
171#17924—431nomaximal, Sylow
172C22×C43—21no—
173C22×C43—24no—
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—42no—
177C22×C43—42no—
178C22×C43—84no—
179C22×C43C2×C4×D411yescharacteristic
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—42no—
185C4×C43C2×#13112yes—
186C4×C43#57712yes—
187Dic43—42no—
188Dic43—42no—
189#3101—431no—
190#2985—431no—
191#2972—431no—
192#1585—432no—
193#1582—432no—
194SD16⋊C8—432no—
195C8×SD16—432no—
196#1572—431no—
197#1490D4311yescharacteristic
198#1485—431no—
199#1453—431no—
200C2×C43—41no—
201C2×C43—44no—
202C2×C43#292911yescharacteristic
203C2×C43#294911yescharacteristic
204C2×C43#295611yescharacteristic
205#533—431no—
206C2×C4×D4C2×D4311yescharacteristic
207#483—432no—
208#476—432no—
209#461—432no—
210#450—432no—
211#446—432no—
212#446—862no—
213C8×Q8—432no—
214C4×SD16—432no—
215C4×SD16—432no—
216C8×D4—432no—
217C8×D4—432no—
218C8×D4—862no—
219#433—862no—
220#432C2×D4311yescharacteristic
221#431—431no—
222#431—431no—
223#431—431no—
224C2×C22⋊C8—862no—
225C4×M16C2×D4311yescharacteristic
226#335—432no—
227#334—432no—
228Q8⋊C8—432no—
229Q8⋊C8—432no—
230D4⋊C8C2×D4312yes—
231D4⋊C8C2×D4312yes—
232#322—431no—
233#322—431no—
234#322—431no—
235C82—431no—
236C43#1792411yescharacteristic, complemented, Sylow
237C22×D4C4×D4311yescharacteristic
238C23×C4—21no—
239C2×SD16—432no—
240C2×SD16—432no—
241C2×M16—21no—
242C22×C8—862no—
243C22×C8—862no—
244C4⋊Q8—431no—
245C4⋊Q8—431no—
246#125—861no—
247C22⋊Q8—432no—
248C22⋊Q8—861no—
249C4×Q8—432no—
250C4×Q8—861no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4C4×D4312yes—
254C4×D4C22×D4312yes—
255#117—861no—
256C2×C4⋊C4C4×D4311yescharacteristic
257C2×C22⋊C4—21no—
258C2×C42C22×D4311yescharacteristic
259#106—432no—
260#106—432no—
261C4⋊C8—432no—
262C4⋊C8—432no—
263C4⋊C8—432no—
264C4⋊C8—862no—
265C4⋊C8—862no—
266C4⋊C8C22×D4312yes—
267#103—432no—
268#103—432no—
269#102—432no—
270#102—432no—
271C22⋊C8—21no—
272C22⋊C8—432no—
273C22⋊C8—432no—
274C22⋊C8—862no—
275C22⋊C8—862no—
276C22⋊C8—861no—
277#97—21no—
278#97—21no—
279#97—862no—
280C4×C8—431no—
281C4×C8—431no—
282C4×C8—431no—
283C4×C8—431no—
284C4×C8—862no—
285C4×C8—861no—
286C4×C8C22×D4311yescharacteristic
287C4×C8C22×D4311yescharacteristic
288C24—21no—
289C2×Q8—432no—
290C2×Q8—861no—
291C2×D4—24no—
292C2×D4—21no—
293C2×D4C2×C4×D4312yes—
294C22×C4—21no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—82no—
298C22×C4C2×C4×D4311yescharacteristic
299C22×C4D4×D4311yescharacteristic
300C22×C4#1062190011yescharacteristic
301SD16—864no—
302SD16—864no—
303M16—42no—
304C2×C8—21no—
305C2×C8—22no—
306C2×C8—21no—
307C2×C8—432no—
308C2×C8—432no—
309C2×C8—432no—
310C2×C8—432no—
311C2×C8—862no—
312C2×C8—3442no—
313C2×C8—3442no—
314C4⋊C4—21no—
315C4⋊C4—432no—
316C4⋊C4—861no—
317C4⋊C4—861no—
318C4⋊C4—862no—
319C4⋊C4—861no—
320C4⋊C4—862no—
321C4⋊C4C2×C4×D4312yes—
322C22⋊C4—22no—
323C22⋊C4—22no—
324C22⋊C4—862no—
325C42—862no—
326C42C2×C4×D4311yescharacteristic
327C42D4×D4311yescharacteristic
328C42#1062190011yescharacteristic
329C42C23×D4311yescharacteristic
330C23—24no—
331C23—22no—
332C23—81no—
333C23—81no—
334C23(C22⋊D43)⋊C411yescharacteristic
335Q8—862no—
336Q8—862no—
337Q8—3441no—
338D4—24no—
339D4—22no—
340D4#1306333314yes—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—82no—
348C2×C4—81no—
349C2×C4—862no—
350C2×C4—862no—
351C2×C4(C22⋊D43)⋊C411yescharacteristic
352C2×C4(C22⋊D43)⋊C411yescharacteristic
353C2×C4(C22⋊D43)⋊C411yescharacteristic
354C2×C4C22×C4×D4311yescharacteristic
355C2×C4C2×D4×D4311yescharacteristic
356C2×C4C2×#1062190011yescharacteristic
357C8—22no—
358C8—41no—
359C8—42no—
360C8—862no—
361C8—862no—
362C8—862no—
363C8—862no—
364C8—1722no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—24no—
369C22—42no—
370C22—42no—
371C22—84no—
372C22C2×(C22⋊D43)⋊C411yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—1722no—
379C4—1722no—
380C4C2×#1306333312yes—
381C4#1458370912yes—
382C2—41no—
383C2—44no—
384C2#1914328511yescharacteristic
385C2#1914345711yescharacteristic
386C2#1914350111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1490C2
socleC22×C43C2×C4×D4
prime radicalC22×D4×C43C2×C4
cosocleC42×C43C24
hypercenter#1490D43
hypocenterC43#17924
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1490

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #19143692C2semidirect
4. #19133449C2semidirect
5. #19133428C2semidirect
6. #19133404C2semidirect
7. #19133398C2semidirect
8. #19133376C2semidirect
9. #19133017C2semidirect
10. #19132892C2semidirect
18. #14583026C22semidirect
19. #14583023C22semidirect
30. #14582651C22semidirect
31. #14582649C22semidirect
32. #14582631C22semidirect
33. #14582631C22semidirect
34. #14582621C22semidirect
35. #14582621C22semidirect
36. #14582620C22semidirect
37. C8×C43⋊C8C22semidirect
236. C43#17924semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191446032
#191436922
#191436192
#191334492
#191334282
#191334042
#191333982
#191333762
#191330172
#191328922
C43×#14902
#1792443